This kind of shows what I do. I built a stand to support a fluorescent light. The light is on chains so I can control the height. It needs to be about 2 above what you are growing.
I cut the bottom out of those small yogurt cups and fill that with potting soil. Ive tried different planting soils and get the best results with plain potting soil. I fill a black plastic tray that you can get from
Walmart with the potting soil and settle the yogurt cups in that. This way the water can drain out of the yogurt cups so it does nto drown them, yet water can wick back up some to keep the soil from drying out. You want the soil damp, not soaking. The seeds will rot instead of sprout if it is too wet, plus the plants that do sprout will die from damping off disease if it is too wet. About once a week after they sprout, I use a weak solution of Miracle Gro in the water. But only once a week. You can over-fertilize them if you get carried away.
To help sprout the plants, I built a box out of plywood and lined it with aluminum foil on the sides and bottom. I put cup hooks on the sides and ran a string of the old time Christmas lights back and forth. This can get hot. I had to remove most of the bulbs from that string of lights to keep it from getting too hot. I just set the black tray full of dirt on this box and it heats the soil. Certain seeds like peppers and tomatoes need warmer soil to germinate. I get much better results if I heat the soil and keep it damp, not wet.
Seeds do not need light to sprout, but they do need light to grow. I keep the clear plastic cover on them to keep the soil from drying out until they sprout, but them remove the cover. Otherwise damping off can be a problem.
About two weeks before I am ready to set them outside, I start to harden them. Plants grown indoors can die from shock if planted directly outdoors. I start putting them in shade and out of the wind for a few hours a day and gradually increase that to all day and all night to toughen them up. Bright sun and especially wind will dry them out and kill them during this hardening off process if you are not careful. Dont let them dry out and dont let the wind hit them. Since I have a constant south wind here, the North side of my workshop works great for this. Dont put the plants where your chickens can get to them. They will destroy them in no time flat.
I start my pepper plants early to mid February. They seem to take forever to sprout and grow really slowly when they do sprout. I start tomato plants about two weeks later. Occasionally the tomato plants get a little big before I set them out, but this gives me time to replant if all the first seeds don't come up. I've been known to repot the plants too if they outgrow those small yogurt cups.